The main purpose of this project is two-fold: (1) to study some important issues in the application of nonparametric repeated significances tests to censored survival data; and (2) to pursue some currently open questions associated with censored data linear rank statistics. The important questions studied in (1) will include: (a) the distribution theory, under various null hypotheses, of repeated significance tests using certain censored data k-sample rank statistics; (b) the implementation of computational procedures for conducting repeated significance procedures; (c) a characterization of stopping rules for repeated tests; and (d) the effect of power and size on a repeated test when accrual stops before follow-up in a randomized clincal trial. In topic (2) the major issues addressed will be (a) the study of adaptive linear rank tests for a generalized logrank family of tests; and (b) the extension of some nonproportional hazards models to include covariates more general than sample membership. The methods used will include asymptotic theory for statistical tests and estimators, Monte Carlo simulations, and numerical analysis.